# The use of cross validation in Dynamic Linear Model (or state space model)

The dynamic linear model has the form as

$$y_t = m(\theta_t, x_t) + \epsilon_t ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ (1)\\ \theta_{t+1} = F \theta_t + R \eta_t,~\eta_t \sim N(\mu_t,\Sigma_t) ~~~~~~(2)$$ where $$m(\theta_t, x_t)$$ is a mapping function, Equation (1) is known as the observation equation and Equation (2) is known as the hidden state equation.

The question is that if I want to compare the prediction performance between the dynamic linear model and another model, say, linear regression model, is it reasonable to use the cross-validation techniques? Or are there other reasonable techniques?

Out-of-sample method, which uses a block of data at the end of the observed series points, is an option, but I am looking for cross-validation like method.